The empirical attenuation functions for Local Magnitude (M_L) currently used in Taiwan have been known for overestimated magnitudes around 0.2 compared with moment magnitude (M_W) for shallow earthquakes (depths ≤ 35 km). Moreover, for deep earthquakes (depths > 35 km), M_L (> 6) can be larger than M_W around 0.5. Based on global observations and seismological theory, M_L is equal to M_W for magnitudes 4 - 6, whereas M_L is smaller than M_W for magnitudes > 6. This indicates that the attenuation functions for the Taiwan region need to be re-calculated. In this study, we used the new data set collected at the upgraded Central Weather Bureau Seismic Network (CWBSN24) from January 2012 to April 2019 and totally there are 692 events with M_L ≥ 3 and 35228 amplitude data used for analysis. To accommodate the complicated tectonic environment in Taiwan, there are four attenuation functions, logA₀(Δ), based on the focal depths and hypocentral distances, which are:

for shallow earthquakes (focal depth, h ≤ 35 km), and

for deep earthquakes (h > 35 km)

where Δ is epicentral distances, R (= ) is hypocentral distance. M_L calculated by using the old attenuation functions for deep and large (M_L > 5.5) earthquakes is larger than that by using the new ones about 0.4. With the new empirical attenuation functions, the relationship between M_L and M_W follows the global observations and also the new M_L avoids the confusion for the public when releasing the official earthquake reports.